Authors: Janev, Marko 
Atanacković, Teodor
Pilipović, Stevan
Obradović, Radovan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Image denoising by a direct variational minimization
Journal: EURASIP Journal on Advances in Signal Processing
Volume: 2011
Issue: 8
Issue Date: 1-Jun-2011
Rank: M23
ISSN: 1687-6180
DOI: 10.1186/1687-6180-2011-8
In this article we introduce a novel method for the image de-noising which combines a mathematically well-posdenes of the variational modeling with the efficiency of a patch-based approach in the field of image processing. It based on a direct minimization of an energy functional containing a minimal surface regularizer that uses fractional gradient. The minimization is obtained on every predefined patch of the image, independently. By doing so, we avoid the use of an artificial time PDE model with its inherent problems of finding optimal stopping time, as well as the optimal time step. Moreover, we control the level of image smoothing on each patch (and thus on the whole image) by adapting the Lagrange multiplier using the information on the level of discontinuities on a particular patch, which we obtain by pre-processing. In order to reduce the average number of vectors in the approximation generator and still to obtain the minimal degradation, we combine a Ritz variational method for the actual minimization on a patch, and a complementary fractional variational principle. Thus, the proposed method becomes computationally feasible and applicable for practical purposes. We confirm our claims with experimental results, by comparing the proposed method with a couple of PDE-based methods, where we get significantly better denoising results specially on the oscillatory regions.
Publisher: Springer Link
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Integrated system for detection and estimation of fire development by real-time monitoring of critical parameters 
Development of Dialogue Systems for Serbian and Other South Slavic Languages 

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